Question

Factor the polynomial by its greatest common monomial factor.

20y^6-15y^4+40y^2=20y
6
−15y
4
+40y
2
=20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared, equals

Answer 1

The greatest common factor of 20y^620y

6

20, y, start superscript, 6, end superscript, -15y^4−15y

4

minus, 15, y, start superscript, 4, end superscript, and 40y^240y

2

40, y, squared is 5y^25y

2

5, y, squared.

[Show me how to find the greatest common factor.]

Now we need to factor 5y^25y

2

5, y, squared out of 20y^6-15y^4+40y^220y

6

−15y

4

+40y

2

20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared.

Hint #22 / 3

\begin{aligned} &\phantom{=}20y^6-15y^4+40y^2 \\\\ &=5y^2(4y^4)+5y^2(-3y^2)+5y^2(8) \\\\ &=5y^2\left(4y^4-3y^2+8\right) \end{aligned}

​

=20y

6

−15y

4

+40y

2

=5y

2

(4y

4

)+5y

2

(−3y

2

)+5y

2

(8)

=5y

2

(4y

4

−3y

2

+8)

​

Hint #33 / 3

In conclusion,

20y^6-15y^4+40y^2=5y^2\left(4y^4-3y^2+8\right)20y

6

−15y

4

+40y

2

=5y

2

(4y

4

−3y

2

+8)20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared, equals, 5, y, squared, left parenthesis, 4, y, start superscript, 4, end superscript, minus, 3, y, squared, plus, 8, right parenthesis

Answer 2

`5 {y}^(2) (4 {y}^(4) - 3 {y}^(2) + 8)`

Explanation:

We want to factor the common monomial out of :

`20 {y}^(6) - 15 {y}^(4) + 40 {y}^(2)`

The greatest common monomial fact is

`5 {y}^(2)`

We factor to get:

`5 {y}^(2) (4 {y}^(4) - 3 {y}^(2) + 8)`

The expression in the parenthesis has no common factor again since we factored the greatest common factor.